Vortices ans Polynomials: Nonuniqueness of the Adler-Moser polynomials for the Tkachenko equation

Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of a system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is obtained that the Adler - Moser polynomial are not unique polynomial solutions of the Tkachenko equation. A generalization of the Tkachenko equation to the case of translating relative equilibria is derived. It is shown that the generalization of the Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers.Comment: 15 pages, 2 figure

Reversing Blood Flows Act through klf2a to Ensure Normal Valvulogenesis in the Developing Heart

Heart valve anomalies are some of the most common congenital heart defects, yet neither the genetic nor the epigenetic forces guiding heart valve development are well understood. When functioning normally, mature heart valves prevent intracardiac retrograde blood flow; before valves develop, there is considerable regurgitation, resulting in reversing (or oscillatory) flows between the atrium and ventricle. As reversing flows are particularly strong stimuli to endothelial cells in culture, an attractive hypothesis is that heart valves form as a developmental response to retrograde blood flows through the maturing heart. Here, we exploit the relationship between oscillatory flow and heart rate to manipulate the amount of retrograde flow in the atrioventricular (AV) canal before and during valvulogenesis, and find that this leads to arrested valve growth. Using this manipulation, we determined that klf2a is normally expressed in the valve precursors in response to reversing flows, and is dramatically reduced by treatments that decrease such flows. Experimentally knocking down the expression of this shear-responsive gene with morpholine antisense oligonucleotides (MOs) results in dysfunctional valves. Thus, klf2a expression appears to be necessary for normal valve formation. This, together with its dependence on intracardiac hemodynamic forces, makes klf2a expression an early and reliable indicator of proper valve development. Together, these results demonstrate a critical role for reversing flows during valvulogenesis and show how relatively subtle perturbations of normal hemodynamic patterns can lead to both major alterations in gene expression and severe valve dysgenesis

Point vortices and classical orthogonal polynomials

Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these equations can be reduced to a single one. It is found that polynomials that are Wronskians of classical orthogonal polynomials solve the latter equation. As a consequence vortex equilibria at a certain choice of background flows can be described with the help of Wronskians of classical orthogonal polynomials.Comment: 20 pages, 12 figure

Openness and archaeology's information ecosystem

The rise of the World Wide Web represents one of the most significant transitions in communicationssince the printing press or even since the origins of writing. To Open Access and Open Data advocates,the Web offers great opportunity for expanding the accessibility, scale, diversity, and quality ofarchaeological communications. Nevertheless, Open Access and Open Data face steep adoption barriers.Critics wrongfully see Open Access as a threat to peer review. Others see data transparency as naivelytechnocratic, and lacking in an appreciation of archaeology’s social and professional incentive structure.However, as argued in this paper, the Open Access and Open Data movements do not gloss oversustainability, quality and professional incentive concerns. Rather, these reform movements offer muchneeded and trenchant critiques of the Academy’s many dysfunctions. These dysfunctions, ranging fromthe expectations of tenure and review committees to the structure of the academic publishing industry, golargely unknown and unremarked by most archaeologists. At a time of cutting fiscal austerity, OpenAccess and Open Data offer desperately needed ways to expand research opportunities, reduce costs andexpand the equity and effectiveness of archaeological communication